Constructing Common Factors from Continuous and Categorical Data

The method of principal components is widely used to estimate common factors in large panels of continuous data. This paper first reviews alternative methods that obtain the common factors by solving a Procrustes problem. While these matrix decomposition methods do not specify the probabilistic structure of the data and hence do not permit statistical evaluations of the estimates, they can be extended to analyze categorical data. This involves the additional step of quantifying the ordinal and nominal variables. The paper then reviews and explores the numerical properties of these methods. An interesting finding is that the factor space can be quite precisely estimated directly from categorical data without quantification. This may require using a larger number of estimated factors to compensate for the information loss in categorical variables. Separate treatment of categorical and continuous variables may not be necessary if structural interpretation of the factors is not required, such as in forecasting exercises.